Quantum field theory of many-body systems : from the origin of sound to an origin of light and electrons / Xiao-Gang Wen.

Format:

Book

Author/Creator:

Wen, Xiao-Gang.

Contributor:

Craig M. Merrihue Memorial Fund.

Series:

Oxford graduate texts

Language:

English

Subjects (All):

Quantum field theory.

Many-body problem.

Physical Description:

xiii, 505 pages : illustrations ; 25 cm.

Place of Publication:

Oxford : Oxford University Press, 2004.

Contents:

1.1 More is different 1

1.2 'Elementary' particles and physics laws 3

1.3 Corner-stones of condensed matter physics 5

1.4 Topological order and quantum order 7

1.5 Origin of light and fermions 9

1.6 Novelty is more important than correctness 11

1.7 Remarks: evolution of the concept of elementary particles 12

2 Path integral formulation of quantum mechanics 14

2.1 Semiclassical picture and path integral 14

2.2 Linear responses and correlation functions 26

2.3 Quantum spin, the Berry phase, and the path integral 43

2.4 Applications of the path integral formulation 50

3 Interacting boson systems 68

3.1 Free boson systems and second quantization 68

3.2 Mean-field theory of a superfluid 71

3.3 Path integral approach to interacting boson systems 77

3.4 Superfluid phase at finite temperatures 99

3.5 Renormalization group 105

3.6 Boson superfluid to Mott insulator transition 120

3.7 Superfluidity and superconductivity 124

3.8 Perturbative calculation of the thermal potential 139

4 Free fermion systems 144

4.1 Many-fermion systems 144

4.2 Free fermion Green's function 152

4.3 Two-body correlation functions and linear responses 164

4.4 Quantized Hall conductance in insulators 179

5 Interacting fermion systems 187

5.1 Orthogonality catastrophe and X-ray spectrum 187

5.2 Hartree-Fock approximation 198

5.3 Landau Fermi liquid theory 203

5.4 Perturbation theory and the validity of Fermi liquid theory 216

5.5 Symmetry-breaking phase and the spin-density-wave state 229

5.6 Nonlinear [sigma]-model 240

6 Quantum gauge theories 250

6.1 Simple gauge theories 250

6.2 Z[subscript 2] lattice gauge theory 252

6.3 U(1) gauge theory and the XY-model in 1 + 2 dimensions 258

6.4 The quantum U(1) gauge theory on a lattice 267

7 Theory of quantum Hall states 275

7.1 The Aharonov-Bohm effect and fractional statistics 275

7.2 The quantum Hall effect 282

7.3 Effective theory of fractional quantum Hall liquids 294

7.4 Edge excitations in fractional quantum Hall liquids 308

8 Topological and quantum order 335

8.1 States of matter and the concept of order 336

8.2 Topological order in fractional quantum Hall states 338

8.3 Quantum orders 348

8.4 A new classification of orders 352

9 Mean-field theory of spin liquids and quantum order 354

9.1 Projective construction of quantum spin-liquid states 355

9.2 The SU(2) projective construction 373

9.3 Topological orders in gapped spin-liquid states 393

9.4 Quantum orders in symmetric spin liquids 397

9.5 Continuous phase transitions without symmetry breaking 411

9.6 The zoo of symmetric spin liquids 414

9.7 Physical measurements of quantum orders 421

9.8 The phase diagram of the J[subscript 1]-J[subscript 2] model in the large-N limit 425

9.9 Quantum order and the stability of mean-field spin liquids 430

9.10 Quantum order and gapless gauge bosons and fermions 434

10 String condensation

an unification of light and fermions 440

10.1 Local bosonic models 443

10.2 An exactly soluble model from a projective construction 444

10.3 Z[subscript 2] spin liquids and string-net condensation 451

10.4 Classification of string-net condensations 458

10.5 Emergent fermions and string-net condensation 466

10.6 The quantum rotor model and U(1) lattice gauge theory 472

10.7 Emergent light and electrons from an SU(N[subscript f]) spin model 487.

Notes:

Includes bibliographical references and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Craig M. Merrihue Memorial Fund.

ISBN:

0198530943

OCLC:

55799875